Hypomixability Theory

TL;DR: Computer scientists can say why the fast fourier transform is fast and why quicksort is quick. Yet when it comes to explaining what’s efficient about the computation that yielded ourselves, we currently draw a blank. Hypomixability theory provides the basis for an answer.

Run a population based recombinative evolutionary algorithm on a real world fitness function; until adaptation tapers off, you will find that the fitness of an offspring is, on average, lower than the mean fitness of its parents. You will find, in other words, that the average fitness of the population goesdown after mixing (recombination) and up after selection. Selection, of course, makes sense—it increases average fitness. But why mixing? What sense does it make to recombine the genes of individuals with above average fitness, especially on epistatic landscapes where recombination is virtually guaranteed to lower average fitness? What computational purpose does mixing serve?

Hypomixability Theory explains why mixing makes computational sense and illuminates how mixing induced reductions in average fitness (the hypo in hypomixability) between parent and offspring populations can be indicative of room for adaptation. The theory is very parsimonious in its assumptions. It does not, for example, assume the presence of building blocks in the fitness landscape. Hypomixability Theory also comes with a prediction and proof of efficient computational learning in a recombinative evolutionary algorithm, making it the first, and currently only, computationally credible explanation for the “endless forms most beautiful and wonderful” that comprise the the sexually reproducing part of the biosphere. Our remarkable species included.